{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finite Volume Discretisation"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we explain the discretisation process that converts an expression tree, representing a model, to a linear algebra tree that can be evaluated by the solvers. \n",
    "\n",
    "We use Finite Volumes as an example of a spatial method, since it is the default spatial method for most PyBaMM models. This is a good spatial method for battery problems as it is conservative: for lithium-ion battery models, we can be sure that the total amount of lithium in the system is constant. For more details on the Finite Volume method, see [Randall Leveque's book](https://books.google.co.uk/books/about/Finite_Volume_Methods_for_Hyperbolic_Pro.html?id=QazcnD7GUoUC&printsec=frontcover&source=kp_read_button&redir_esc=y#v=onepage&q&f=false).\n",
    "\n",
    "This notebook is structured as follows:\n",
    "\n",
    "1. **Setting up a discretisation**. Overview of the parameters that are passed to the discretisation\n",
    "2. **Discretisations and spatial methods**. Operations that are common to most spatial methods:\n",
    "    - Discretising a spatial variable (e.g. $x$)\n",
    "    - Discretising a variable (e.g. concentration)\n",
    "3. **Example: Finite Volume operators**. Finite Volume implementation of some useful operators: \n",
    "    - Gradient operator\n",
    "    - Divergence operator\n",
    "    - Integral operator\n",
    "4. **Example: Discretising a simple model**. Setting up and solving a simple model, using Finite Volumes as the spatial method\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting up a Discretisation"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first import `pybamm` and some useful other modules, and change our working directory to the root of the `PyBaMM` folder:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install \"pybamm[plot,cite]\" -q    # install PyBaMM if it is not installed\n",
    "import os\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import pybamm\n",
    "\n",
    "os.chdir(pybamm.__path__[0] + \"/..\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To set up a discretisation, we must create a geometry, mesh this geometry, and then create the discretisation with the appropriate spatial method(s). The easiest way to create a geometry is to the inbuilt battery geometry:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "parameter_values = pybamm.ParameterValues(\n",
    "    values={\n",
    "        \"Negative particle radius [m]\": 0.5,\n",
    "        \"Positive particle radius [m]\": 0.6,\n",
    "        \"Negative electrode thickness [m]\": 0.3,\n",
    "        \"Separator thickness [m]\": 0.2,\n",
    "        \"Positive electrode thickness [m]\": 0.3,\n",
    "    }\n",
    ")\n",
    "\n",
    "geometry = pybamm.battery_geometry()\n",
    "parameter_values.process_geometry(geometry)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then use this geometry to create a mesh, which for this example consists of uniform 1D submeshes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "submesh_types = {\n",
    "    \"negative electrode\": pybamm.Uniform1DSubMesh,\n",
    "    \"separator\": pybamm.Uniform1DSubMesh,\n",
    "    \"positive electrode\": pybamm.Uniform1DSubMesh,\n",
    "    \"negative particle\": pybamm.Uniform1DSubMesh,\n",
    "    \"positive particle\": pybamm.Uniform1DSubMesh,\n",
    "    \"current collector\": pybamm.SubMesh0D,\n",
    "}\n",
    "\n",
    "var = pybamm.standard_spatial_vars\n",
    "var_pts = {var.x_n: 15, var.x_s: 10, var.x_p: 15, var.r_n: 10, var.r_p: 10}\n",
    "mesh = pybamm.Mesh(geometry, submesh_types, var_pts)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can use the mesh to create a discretisation, using Finite Volumes as the spatial method for this example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "spatial_methods = {\n",
    "    \"macroscale\": pybamm.FiniteVolume(),\n",
    "    \"negative particle\": pybamm.FiniteVolume(),\n",
    "    \"positive particle\": pybamm.FiniteVolume(),\n",
    "}\n",
    "disc = pybamm.Discretisation(mesh, spatial_methods)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discretisations and Spatial Methods"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Spatial Variables"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Spatial variables, such as $x$ and $r$, are converted to `pybamm.Vector` nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_disc is a <class 'pybamm.expression_tree.vector.Vector'>\n",
      "r_disc is a <class 'pybamm.expression_tree.vector.Vector'>\n"
     ]
    },
    {
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      "text/plain": [
       "<Figure size 1300x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set up\n",
    "macroscale = [\"negative electrode\", \"separator\", \"positive electrode\"]\n",
    "x_var = pybamm.SpatialVariable(\"x\", domain=macroscale)\n",
    "r_var = pybamm.SpatialVariable(\"r\", domain=[\"negative particle\"])\n",
    "\n",
    "# Discretise\n",
    "x_disc = disc.process_symbol(x_var)\n",
    "r_disc = disc.process_symbol(r_var)\n",
    "print(f\"x_disc is a {type(x_disc)}\")\n",
    "print(f\"r_disc is a {type(r_disc)}\")\n",
    "\n",
    "# Evaluate\n",
    "x = x_disc.evaluate()\n",
    "r = r_disc.evaluate()\n",
    "\n",
    "f, (ax1, ax2) = plt.subplots(1, 2, figsize=(13, 4))\n",
    "\n",
    "ax1.plot(x, \"*\")\n",
    "ax1.set_xlabel(\"index\")\n",
    "ax1.set_ylabel(r\"$x$\")\n",
    "\n",
    "ax2.plot(r, \"*\")\n",
    "ax2.set_xlabel(\"index\")\n",
    "ax2.set_ylabel(r\"$r$\")\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define `y_macroscale`, `y_microscale` and `y_scalar` for evaluation and visualisation of results below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_macroscale = x**3 / 3\n",
    "y_microscale = np.cos(r)\n",
    "y_scalar = np.array([[5]])\n",
    "\n",
    "y = np.concatenate([y_macroscale, y_microscale, y_scalar])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variables"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we will work with three variables `u`, `v`, `w`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = pybamm.Variable(\n",
    "    \"u\", domain=macroscale\n",
    ")  # u is a variable in the macroscale (e.g. electrolyte potential)\n",
    "v = pybamm.Variable(\n",
    "    \"v\", domain=[\"negative particle\"]\n",
    ")  # v is a variable in the negative particle (e.g. particle concentration)\n",
    "w = pybamm.Variable(\n",
    "    \"w\"\n",
    ")  # w is a variable without a domain (e.g. time, average concentration)\n",
    "\n",
    "variables = [u, v, w]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before discretising, trying to evaluate the variables raises a `NotImplementedError`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "method self.evaluate() not implemented for symbol u of type <class 'pybamm.expression_tree.variable.Variable'>\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    u.evaluate()\n",
    "except NotImplementedError as e:\n",
    "    print(e)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For any spatial method, a `pybamm.Variable` gets converted to a `pybamm.StateVector` which, when evaluated, takes the appropriate slice of the input vector `y`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Discretised u is the StateVector y[0:40]\n",
      "Discretised v is the StateVector y[40:50]\n",
      "Discretised w is the StateVector y[50:51]\n"
     ]
    }
   ],
   "source": [
    "# Pass the list of variables to the discretisation to calculate the slices to be used (order matters here!)\n",
    "disc.set_variable_slices(variables)\n",
    "\n",
    "# Discretise the variables\n",
    "u_disc = disc.process_symbol(u)\n",
    "v_disc = disc.process_symbol(v)\n",
    "w_disc = disc.process_symbol(w)\n",
    "\n",
    "# Print the outcome\n",
    "print(f\"Discretised u is the StateVector {u_disc}\")\n",
    "print(f\"Discretised v is the StateVector {v_disc}\")\n",
    "print(f\"Discretised w is the StateVector {w_disc}\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the variables have been passed to `disc` in the order `[u,v,w]`, they each read the appropriate part of `y` when evaluated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1300x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_fine = np.linspace(x[0], x[-1], 1000)\n",
    "r_fine = np.linspace(r[0], r[-1], 1000)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(13, 4))\n",
    "ax1.plot(x_fine, x_fine**3 / 3, x, u_disc.evaluate(y=y), \"o\")\n",
    "ax1.set_xlabel(\"x\")\n",
    "ax1.legend([\"x^3/3\", \"u\"], loc=\"best\")\n",
    "\n",
    "ax2.plot(r_fine, np.cos(r_fine), r, v_disc.evaluate(y=y), \"o\")\n",
    "ax2.set_xlabel(\"r\")\n",
    "ax2.legend([\"cos(r)\", \"v\"], loc=\"best\")\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w = [[5.]]\n"
     ]
    }
   ],
   "source": [
    "print(f\"w = {w_disc.evaluate(y=y)}\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finite Volume Operators"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gradient operator\n",
    "\n",
    "The gradient operator is converted to a Matrix-StateVector multiplication. In 1D, the gradient operator is equivalent to $\\partial/\\partial x$ on the macroscale and $\\partial/\\partial r$ on the microscale. In Finite Volumes, we take the gradient of an object on nodes (shape (n,)), which returns an object on the edges (shape (n-1,)). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "@\n",
      "├── Sparse Matrix (39, 40)\n",
      "└── y[0:40]\n"
     ]
    }
   ],
   "source": [
    "grad_u = pybamm.grad(u)\n",
    "grad_u_disc = disc.process_symbol(grad_u)\n",
    "grad_u_disc.render()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Matrix in `grad_u_disc` is the standard `[-1,1]` sparse matrix, divided by the step sizes `dx`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gradient matrix is:\n",
      "\n",
      "1/dx *\n",
      "[[-1.  1.  0. ...  0.  0.  0.]\n",
      " [ 0. -1.  1. ...  0.  0.  0.]\n",
      " [ 0.  0. -1. ...  0.  0.  0.]\n",
      " ...\n",
      " [ 0.  0.  0. ...  1.  0.  0.]\n",
      " [ 0.  0.  0. ... -1.  1.  0.]\n",
      " [ 0.  0.  0. ...  0. -1.  1.]]\n"
     ]
    }
   ],
   "source": [
    "macro_mesh = mesh.combine_submeshes(*macroscale)\n",
    "print(\"gradient matrix is:\\n\")\n",
    "print(\n",
    "    f\"1/dx *\\n{macro_mesh.d_nodes[:, np.newaxis] * grad_u_disc.children[0].entries.toarray()}\"\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When evaluated with `y_macroscale=x**3/3`, `grad_u_disc` is equal to `x**2` as expected:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zcxNff/217hgA8eWXX+qN6927t3jvvff0jm3atEn4+PjofnZ3dxcbN27UG7N9+3bRoEEDcffuXSGEEMnJyUKSJL3rWZpoVvS4fPmy3mt+9tlnwtHRUcyaNUs4OzuLP/74Qy+mbt26iQkTJogJEyaIbt26iU2bNlX5XKlRo0aJevXqCQBiyJAh5X6v3n33XfHkk0/qHfvtt9+Ei4uLsLOzE+7u7uLbb78td52/+uoroVAodIlmWUxGiExw6ivtP5bLfFep56mEZp679nkzYWwyYtu3aWRsrZyamori4mKEhYXpjrm7u6Nt27Z640JDQ8udu3PnTvTq1Qve3t5wdXXFnDlzkJaWpnv+9OnTCA8P1zun7M937tzR3U6ojnr16uH27dsGn7t+/TouXbqEiRMnwtXVVfdYuHAhzp8/DwBo3Lgx+vfvj82bNwMALly4gMOHD2PMmDG610lKSsKwYcPg7+8PNzc3PPzwwwCg91lNlZmZiaioKLRp0wbu7u5wd3dHQUFBla95/PhxLFiwQO/zPP/880hPT9ddB0PXdPjw4bC3t8eXX34JAFi3bh0eeeQRvds/rVq1qvTRpEkTvdd85pln8OSTTyI6OhqLFy9GmzZ/1xDIzMxEQkICevfujd69eyMhIUF3a6uy50otXboUJ06cwK5du3D+/HlMnz5d7/mvvvpKd4umVNu2bZGcnIwjR47gxRdfxLhx45CSkqI3pl69etBoNCgsLKz0OhNRFTRqYPcbMNRpRoF73WZ2z7S4TRi2XYFVxtbK4t49f0mSDB4v5eLiovfzkSNHMGrUKMyfPx8DBgyAu7s7tm3bhsWLF5v0/h4eHjh58qTesdIdIPfHUHYtSqmcnBzdeoOySndNrFmzBt26ddN7zs7u79LDY8aMwdSpU7FixQps2bIFDz30EDp16gQAuHXrFiIiIhAREYFPP/0UjRs3RlpaGgYMGFDhQl6FQlHu+pWNf/z48bh+/TpiYmLg7+8PR0dHhIeHV7k4WKPRYP78+XjyySfLPVeagHh4eODGjRt6zymVSowdOxbr16/Hk08+iS1btiAmJkZvjKura6Xv3bt3b70dKrdv38bx48dhZ2eHc+fO6Y0tmzy4ubnpjlX2XClvb294e3sjMDAQjRo1Qu/evTFnzhz4+PggIyMDJ06c0FtnVPoZW7VqBUCbPB87dgzLli3Dxx9/rBuTk5MDZ2dn1KtnYfexiczNxUPl1zjqEUDeFe04M622aohtJyP+PbSNgvLSYSjL1LZW9q2V1sotW7aEg4MDjh49Cj8/PwBAXl4ezp07hz59+lR43sGDB+Hv769bsAgAFy9e1BvTrl07HDlyBJGRkbpj9y8oBIDg4GCsXLkSQghdQlSaXKSnp6NBgwYAtAtYy7p79y7Onz+P4OBggzF6eXmhSZMmSE1N1ZvpKGv48OF44YUXsHv3bmzZsgVjx47VPXfmzBlkZWVh0aJFuutTdiFoWY0bN0ZGRobeZyob//79+xEbG4tBgwYBAC5duoSsrCy9MQ4ODlCr9f9V0aVLF/zxxx+6L11DgoODy80IAMCkSZMQFBSE2NhYFBcXl0toDF3j+5X9An/11VehUCjw3XffYdCgQRg8eDD69u2rN2b8+PEVvl5lz92vNLErnc2Ii4tDeHg4PDw8qjyv7AzI77//ji5duhj1vkRUCRln9GuTbScjCjvgsfe1u2YgQT8hqd3Wym5ubhg3bhxmzJiBhg0bwtPTE/PmzYNCoSg3W3K/Vq1aIS0tDdu2bUPXrl3x7bff6m4BlJo6dSrGjRuH0NBQ9OrVC5s3b8apU6fQokUL3ZhHHnkEt27dwqlTpxAUFKR7bT8/P7z99ttYuHAhzp07Z3DG5ciRI7oZhVKRkZFo0qQJoqOjAWh3tkyZMgUqlQoDBw5EYWEhEhMTcePGDd2/xl1cXDBs2DDMmTMHp0+fxujRo3Wv16xZMyiVSqxYsQJRUVH4/fff8c4771R6TR9++GFcv34dH3zwAZ5++mns3r0b3333HVQqld7127RpE0JDQ5GXl4cZM2aU+7Jv3rw5fvjhB/Ts2ROOjo5o0KAB5s6di8cffxx+fn545plnoFAo8Ntvv+HkyZNYuHAhAGDAgAH45JNPysXVrl07dO/eHW+88QYmTJhQ7v0qS3DK+vbbb7Fu3TocPnwYXbp0wcyZMzFu3Dj89ttvugSyOuLj43Ht2jV07doVrq6uSElJweuvv46ePXvqbinFxcVh2LBheue9+eabGDhwIPz8/JCfn49t27Zh79692L17t964/fv3IyIiotrxEdE9Ms7o16paXrtSI2ptAWspA6uSxeJ2tb4IKC8vT4wePVo4OzsLb29vsWTJEhEWFiZmzpwphNAuYF26dGm582bMmCEaNWokXF1dxciRI8XSpUuFu7u73ph3331XeHh4CFdXVzFu3Djx+uuvl1vcOWrUKN17lTpw4IDo0KGDcHJyEr179xY7duwot4D1X//6l3jhhRf0zuvTp48YN26c3rHNmzeLzp07C6VSKRo0aCD+8Y9/iC+++EJvzLfffisAiH/84x/lPueWLVtE8+bNhaOjowgPDxdxcXECgEhKShJCGF5wu3LlSuHn5ydcXFxEZGSkePfdd/UWsJ44cUKEhoYKR0dH0bp1a7Fjx45y1zkuLk60atVK2Nvb6527e/du0aNHD1GvXj2hUqlEWFiYWL16te75nJwcUa9ePXHmzJlyn2Xt2rUCgDh69Gi554yVmZkpvLy89BbSFhcXi7CwMDFixIhqv64QQvz4448iPDxcuLu7CycnJ9G6dWvxxhtv6K5tQUGBcHJyEmfPntU7b8KECcLf318olUrRuHFj8eijj4o9e/bojbl8+bJwcHAQly5dqvD9uYCVyEjqElH0QVuhnivPLlBTGbuAVRLCxGIHMsjLy4O7uztyc3P1/pULaG8ZXLhwAQEBAQ+0IBMateytlW/duoUmTZpg8eLFmDhxYq2/38mTJ9GvXz/8+eefcHMzrmTw9evXERgYiMTERAQEBNRyhJbn9ddfR25urt56CQB49913sW3btnLrdCzFF198gbfeesvgbaiqzJgxA7m5uVi9enWFY2rs95jIyt0tVuP9pR9gzq1FgFS2WNi9WfURG4H2Qw2cXfcq+/6+n23vprmfwk672KfD09o/6yARSUpKwtatW3H+/HmcOHFCt76i7FR4benQoQM++OADvYJmVblw4QJiY2OZiFRg9uzZ8Pf31605KSgowLFjx7BixQpMmTJF5uiqz9XVFe+//361zvX09KzyFhsRGSc6/jTW53TEG3YzIFx99Z9U+ZpVImIKzozIKCkpCZMmTcIff/wBpVKJkJAQLFmyBB06dJA7NKoh48ePx9atWzF8+HBs2bJFbzcR/c2Sf4+J6spPZzLx3IZjAIANz3XFw60byT6jXxVjZ0ZsewGrzIKDg3H8+HG5w6BaVFnDOiIiY13PL8SMnb8CAJ7r2RwPt/XUPmFB23crw9s0REREZkwIgRk7f0VWQRECvd3wxmOBcodU46wmGbGAu01EVAH+/hJV7JNDf2HvH9ehtFdg2ahgODmY162YmmDxyYiDgwMAVFianIjMX+nvb+nvMxFpncnIw3vfnQEAzB7UDm29jdv5aGksfs2InZ0d6tevr+ux4ezsXGnRMCIyH0II3L59G5mZmahfvz4X+BLd526xGlO3JqOoRINH2jZGZLi/3CHVGotPRgBtPw0A5Zp+EZFlqF+/vu73mMhmlal39f5v7vjjWj48XJX44OlOVv0PbatIRiRJgo+PDzw9PSts7EZE5snBwYEzIkQpcdpuvPc1wXteNMRVRSRGPf0SGrs5yhhc7bOKZKSUnZ0d/6NGRESWJSXuXo80/YXc3sjBKmUMJE0IAMsrZGYKi1/ASkREZLE0au2MiIHO8QoJACRg90ztOCvGZISIiEguFw/p3ZopS4IA8q5ox1kxJiNERERyKbhWs+MsFJMRIiIiubh61ew4C8VkhIiISC7+PSBUvgZWjJSSAFUTbRM8K8ZkhIiISC4KOxxsNQNCAJpyGcm9uiKPLTK7brw1jckIERGRTM5dy8ekYz54sXgabjt56j+p8gVGbATaW/e2XsDK6owQERFZirvFary8JQl3izW43XoQnMfNAS4d1lVghX8Pq58RKcVkhIiISAYLv025V+7dEUtGdIbC3h4I6C13WLLgbRoiIqI6tvv3dHx6JA0AsGREJ6sv914VJiNERER16PKN23h9528AgKg+LfGPNo1ljkh+TEaIiIjqSIlag2nbkpF3twSd/erj1Yg2codkFpiMEBER1ZFlP5xD4sUbcHO0x4p/BsPBjl/DABewEhER1R6NWttXpuAafs9zQuxPAoAC7z3ZAX4NneWOzmwwGSEiIqoNKXHajrz3GuEFAdivbIgf/KdjSKfB8sZmZjg/REREVNNS4oDPIst15PWWcvBs2hzt86TDZISIiKgmadTaGREDHWcUuFfkffdM7TgCwGSEiIioZl08VG5GRJ8A8q5oxxGAaiYjsbGxCAgIgJOTE0JCQrB///5Kx2/evBmdOnWCs7MzfHx88NxzzyE7O7taARMREZm1gms1O84GmJyMbN++HdOmTcPs2bORlJSE3r17Y+DAgUhLSzM4/sCBA4iMjMTEiRNx6tQp7NixA8eOHcOkSZMeOHgiIiKz4+pVs+NsgMnJyJIlSzBx4kRMmjQJ7dq1Q0xMDPz8/LBy5UqD448cOYLmzZtjypQpCAgIQK9evfDCCy8gMTGxwvcoLCxEXl6e3oOIiMgi+PdAvtITmvJLRu6RAFUTbSM8AmBiMlJUVITjx48jIiJC73hERAQOHTJ876tHjx64fPky4uPjIYTAtWvXsHPnTgweXPG2pujoaLi7u+sefn5+poRJREQkm0OpNzDj1mgAgNAuV73PvZ8fW2QzHXmNYVIykpWVBbVaDS8v/aklLy8vZGRkGDynR48e2Lx5M0aOHAmlUglvb2/Ur18fK1asqPB9Zs2ahdzcXN3j0qVLpoRJREQki8z8u5iyLRm71WH4tNlCSCof/QEqX2DERqD9UHkCNFPVKnomSfqZnhCi3LFSKSkpmDJlCubOnYsBAwYgPT0dM2bMQFRUFNauXWvwHEdHRzg62nYHQyIisixqjcC0bcnIKihEWy83PDN2MmA/WVeBFa5e2lsznBEpx6RkxMPDA3Z2duVmQTIzM8vNlpSKjo5Gz549MWPGDABAx44d4eLigt69e2PhwoXw8fExeB4REZElWfHjORw6nw1npR0+GtMF9ZT3ko6A3vIGZgFMuk2jVCoREhKChIQEveMJCQno0cPwQpzbt29DodB/Gzs77f9BQlS4uoeIiMhiHPozC8t+OAcAeO+JDmjl6SpzRJbF5N0006dPx3//+1+sW7cOp0+fxiuvvIK0tDRERUUB0K73iIyM1I0fMmQIvvjiC6xcuRKpqak4ePAgpkyZgrCwMPj6+tbcJyEiIpJB6ToRIYBRXf0wPLiJ3CFZHJPXjIwcORLZ2dlYsGAB0tPTERQUhPj4ePj7+wMA0tPT9WqOjB8/Hvn5+fi///s/vPrqq6hfvz769u2L999/v+Y+BRERkQzuXycS6O2Gt4c+JHdIFkkSFnCvJC8vD+7u7sjNzYVKpZI7HCIislUatd6C1KXnPLDsx1Q4K+0Q93Iv3p4pw9jv72rtpiEiIrI5KXHaBnj39Z0ZKRrijCISA5/4FxORB8BkhIiIqCopccBnkSjbidcbOViljIHkGAKAa0Wqi117iYiIKqNRa2dEUH5Vg0ICAAnYPVM7jqqFyQgREVFlLh7SuzVTlgQB5F3RjqNqYTJCRERUmYJrNTuOymEyQkREVBlXwxXGqz2OymEyQkREVBn/HtC4+UJT4QAJUDXR9p2hamEyQkREVAkhKfBf138BAgYSkntNYh9bxAZ4D4DJCBERUSXWHriA9y60wb/Vr6DEuUxzV5UvMGIj0H6oPMFZCdYZISIiqkDiXzlY9N0ZAEDYoPFQdp+jV4EV/j04I1IDmIwQEREZkFVQiJe2nECJRmBIJ19EhvsDkgQE9JY7NKvD2zRERERllKg1+PeWJFzLK0QrT1cserIDJEmSOyyrxWSEiIiojCUJZ3E4NRvOSjuserYLXBx5I6E2MRkhIiK6z+7fMxC79zwAYNFTHdHK003miKwfUz0iIrJtGrVuUeqVEhVe36XtMTOhZwCGdvKVOTjbwGSEiIhsV0qctgnevd4zTQDsRkNs9Z6MKYMGyhubDeFtGiIisk0pccBnkeWa4HlLOZh+8104/PGNTIHZHiYjRERkezRq7YwIRLmnFLhXV3X3TO04qnVMRoiIyPZcPFRuRkSfAPKuaMdRrWMyQkREtqfgWs2OowfCZISIiGyPq1fNjqMHwmSEiIhsjmgWjhv2jaEpv2TkHglQNdH2nqFax2SEiIhszidHLmHm7TEAAIGyZd7v/fzYIjbBqyNMRoiIyKYcvZCDhd+exveaMPzY8T+QVD76A1S+wIiNQPuh8gRog1j0jIiIbEZG7l1M3qztxDu0ky8efXIQICboKrDC1Ut7a4YzInWKyQgREdmEwhI1Xtx8HFkFhQj0dsOip+514pXsgIDecodn03ibhoiIrJ4QAnN3nUJS2k2onOzx8dgQOCv573FzwWSEiIis3qYjF7E98RIUErD8n8Hwb+Qid0h0H6aFRERkXe7rwgtXLxwuaYv5X6cAAGYODMTDbT1lDpDKYjJCRETWo0wXXgAIQCP0w1jU6zwcz/duIWNwVBEmI0REZB1Ku/CWaX7nKbKxShmD4oeCIUnB8sRGleKaESIisnyVdeGVAECCMuFNduE1U0xGiIjI8lXRhVdiF16zxmSEiIgsH7vwWjQmI0REZPnYhdeiMRkhIiLL598DGjdfaCocwC685ozJCBERWbwSIWGFchIgYCAhYRdec8dkhIiILN4H3/+BpVcCMU0zHWoXduG1NKwzQkREFu3LpMtYvS8VADDgmX/BIegtduG1MExGiIjIYh2/eANv7DwJAHjpkZYY3PHerAi78FoU3qYhIiKLdPnGbbywKRFFag0i2nvh1f5t5Q6JqonJCBERWZxbhSWY9EkisgqK0M5HhaUjO0OhkOQOi6qJt2mIiMj83deJV+PiiVf2O+JMRj48XB3x33GhcHHk15kl4/97RERk3sp04lUAeFs0hNJhPCZETkGT+vXkjY8eGJMRIiIyXxV04vVGDlbYLYVUEAyAW3YtHdeMEBGReaqiE68EALtnshOvFWAyQkRE5qmKTrxgJ16rwWSEiIjMEzvx2gwmI0REZJ7YiddmMBkhIiLz5N8DeUpPaMovGbmHnXitBZMRIiIySztOXMWMgtEAAIGyBc3YideaMBkhIiKzc/h8Nt788iS+14Thm3bvQ1KxE681Y50RIiIyK+evFyDq0+MoVgsM7uiDx0cMAvA8O/FaMSYjRERkNrILCvHc+mPIvVOMLs3qY/Ezne71nLFjJ14rxts0RERkFu4Wq/GvTceRlnMbzRo6Y01kKJwcOPthC5iMEBGR7DQagdd2/IrjF29A5WSPdeO7opGro9xhUR3hbRoiIqp793XhhasXlv7RCN/8lg57hYRVY0PQytNV7gipDjEZISKiulWmCy8A/FM0xFlFJPo9OQk9WnrIGBzJoVq3aWJjYxEQEAAnJyeEhIRg//79lY4vLCzE7Nmz4e/vD0dHR7Rs2RLr1q2rVsBERGTBSrvwluk5440crFLG4BnnJJkCIzmZPDOyfft2TJs2DbGxsejZsyc+/vhjDBw4ECkpKWjWrJnBc0aMGIFr165h7dq1aNWqFTIzM1FSUvLAwRMRkQWpoguvgKTtwhs4mNt2bYwkhKiw0K4h3bp1Q5cuXbBy5UrdsXbt2mH48OGIjo4uN3737t0YNWoUUlNT0bBhQ6Peo7CwEIWFhbqf8/Ly4Ofnh9zcXKhUKlPCJSIic3FhP/DJ41WPG/cNt/Faiby8PLi7u1f5/W3SbZqioiIcP34cERERescjIiJw6JDhFs5xcXEIDQ3FBx98gCZNmqBNmzZ47bXXcOfOnQrfJzo6Gu7u7rqHn5+fKWESEZE5YhdeqoBJt2mysrKgVqvh5aXfIdHLywsZGRkGz0lNTcWBAwfg5OSEL7/8EllZWZg8eTJycnIqXDcya9YsTJ8+Xfdz6cwIERFZMHbhpQpUazeNJOk3LBJClDtWSqPRQJIkbN68Ge7u7gCAJUuW4Omnn8ZHH32EevXqlTvH0dERjo7cX05EZFXudeF1LcyEwuBXhqTtOcMuvDbHpNs0Hh4esLOzKzcLkpmZWW62pJSPjw+aNGmiS0QA7RoTIQQuX75cjZCJiMgSrT+cxi68ZJBJyYhSqURISAgSEhL0jickJKBHD8OZbM+ePXH16lUUFBTojp09exYKhQJNmzatRshERGRpvjuZjgXfpOB7TRi+f+hDduElPSbvptm+fTvGjh2LVatWITw8HKtXr8aaNWtw6tQp+Pv7Y9asWbhy5Qo2btwIACgoKEC7du3QvXt3zJ8/H1lZWZg0aRL69OmDNWvWGPWexq7GJSIi85P4Vw5G//cXFJVo8Gz3ZnhnWBAkoWEXXhtg7Pe3yWtGRo4ciezsbCxYsADp6ekICgpCfHw8/P39AQDp6elIS0vTjXd1dUVCQgL+/e9/IzQ0FI0aNcKIESOwcOHCanwsIiKyJH9mFmDiJ4koKtGgXzsvzB8apF1jKLELL/3N5JkROXBmhIjI8mTm38UTHx3ClZt30NmvPrY+3x31lJz9sCW1NjNCRERUTpnGdwXeYXhu/TFcuXkHzRs5Y+24UCYiVCEmI0RE9GAMNL4rtPNA0zvPIsOlFz6ZEIZGrizXQBVjMkJERNVX2viuTL+ZBiVZWOkQg4sPB8K/kYs8sZHFqFbXXiIioqoa30mShIBj72jHEVWCyQgREVXPxUN6t2bKkiCAvCvacUSVYDJCRETVw8Z3VEOYjBARUfWw8R3VECYjRERUPf49UOziA02FAyRA1YSN76hKTEaIiKharuYVYU7hWEDAQELCxndkPCYjRERkshu3ijB27S/YVtAZ8+vNBFx99Qew8R2ZgHVGiIjIJLeLSvDchmM4f/0WfNyd8K+oaVCoXmfjO6o2JiNERGS0YrUGL356AsmXbsK9ngM2TghDk/r1tE+y8R1VE2/TEBGRUTQagRk7fsXPZ6/DyUGBdeO7orWXm9xhkRXgzAgRERl2X/M74eqJ935vgF3JV2GnkLByTAhC/BvIHSFZCSYjRERUXpnmdxKACaIhLikiMeDp5/FIoKe88ZFVYTJCRET6Kmh+540crFIug+QUAqCpLKGRdeKaESIi+ltVze8AYPdMNr+jGsVkhIiI/lZF8zuw+R3VAiYjRET0Nza/IxkwGSEior+x+R3JgMkIERHpXHTthGtoBE35JSP3sPkd1TwmI0REBADIyL2LMesSMbdoLCQJEKXN7nTY/I5qB5MRIiJCzq0iPLv2F1y+cQdnGjyMvKHrIKl89Aex+R3VEtYZISKycfl3izFu3VH8mVkAH3cnfDqxG9wbOgOdh7P5HdUJJiNERDbsbrEaEz9JxMkruWjoosSmid3g19BZ+6TCjs3vqE4wGSEishX39ZqBqxeKmnTHi5uTcPRCDtwc7bFxQhhaebrKHSXZICYjRES2oEyvGQC4Zd8Yyttj4OTQHWvHd0VQE3cZAyRbxmSEiMjaVdBrxr34OlY6xCCl9/8hKKChPLERgbtpiIisW1W9ZiQJQb9Fs9cMyYrJCBGRNaui14zEXjNkBpiMEBFZM/aaIQvAZISIyJqx1wxZACYjRETWzL8HChy92GuGzBqTESIiK7bxl0t4Nf+fAAwtYWWvGTIPTEaIiKzU9mNpmPvVKXyvCUNc20Xa3jL3Y68ZMhOsM0JEZIV2JV3BzC9OAgAm9grAsMGDIIl/sdcMmSUmI0REVubb39Ix/bNkCAE8270Z3hrcDpIkARJ7zZB5YjJCRGTJyvSbSbjVElO3JUMjgBGhTbFgaJA2ESEyY0xGiIgslYF+M0GiIR5FJJw6D0f0kx2hUDARIfPHZISIyBJV0G/GCzlYpYyBJqgL7BTB8sRGZCLupiEisjRV9JsBJNjtmcV+M2QxmIwQEVka9pshK8NkhIjI0rDfDFkZJiNERJaG/WbIyjAZISKyMD/cbol00ZD9ZshqMBkhIrIgP565hhe3/Iq3iyMhSYBA2a277DdDlofJCBGRhfjxzDVEbTqBIrUGdg8NhfrpjZBUPvqD2G+GLBDrjBARWYAfTl/Di59qE5FBHbyxbFQw7O1CgPaPs98MWTwmI0RE5qRMeXf498DulEz8e2sSitUCA4O0iYiD3b2JbQX7zZDlYzJCRGQuDJR3v+Pkja/y/4lidVcM6eSLJSM6/Z2IEFkJ/o0mIjIHpeXdyxQzc7yTgY/sl+LtVucRM7IzExGySvxbTUQktyrKu0sSMC5vFeygqfvYiOoAkxEiIrlVWd4dkFjenawYkxEiIrmxvDvZOCYjRERyY3l3snFMRoiIZCaahSNf6cny7mSzmIwQEclICIHo78/htYLR2p9Z3p1sEJMRIiKZaDQCc776Hav3peJ7TRh+7ryY5d3JJlUrGYmNjUVAQACcnJwQEhKC/fv3G3XewYMHYW9vj86dO1fnbYmIrEaxWoPpnyXj0yNpkCQg+skOeOSJScC034Fx3wBPrdX+Oe0kExGyeiZXYN2+fTumTZuG2NhY9OzZEx9//DEGDhyIlJQUNGvWrMLzcnNzERkZiUcffRTXrnFFOBHZkDIl3u/6dsPL237D/05fg71CwpKRnTG0k692LMu7kw2ShBAVLpkypFu3bujSpQtWrlypO9auXTsMHz4c0dHRFZ43atQotG7dGnZ2dti1axeSk5MrHFtYWIjCwkLdz3l5efDz80Nubi5UKpUp4RIRyctAifdshQfevPss9iq6Y+WzXdA3kLtkyDrl5eXB3d29yu9vk27TFBUV4fjx44iIiNA7HhERgUOHKi7Gs379epw/fx7z5s0z6n2io6Ph7u6ue/j5+ZkSJhGReaigxHsDdRZWOsQg7tEcJiJEMDEZycrKglqthpeX/i+Pl5cXMjIyDJ5z7tw5zJw5E5s3b4a9vXF3hWbNmoXc3Fzd49KlS6aESUQkvypLvEtom/SudhyRjatW115J0t96JoQodwwA1Go1Ro8ejfnz56NNmzZGv76joyMcHR2rExoRkXmossS7AEpLvHONCNk4k5IRDw8P2NnZlZsFyczMLDdbAgD5+flITExEUlISXn75ZQCARqOBEAL29vbYs2cP+vbt+wDhExGZKZZ4JzKaSbdplEolQkJCkJCQoHc8ISEBPXqUrwyoUqlw8uRJJCcn6x5RUVFo27YtkpOT0a1btweLnojIXLHEO5HRTL5NM336dIwdOxahoaEIDw/H6tWrkZaWhqioKADa9R5XrlzBxo0boVAoEBQUpHe+p6cnnJycyh0nIrImh0raoIVoBE9kQ1H+Lja0Jd59WeKdCNVIRkaOHIns7GwsWLAA6enpCAoKQnx8PPz9/QEA6enpSEtLq/FAiYgsRfzJdEzbloxHxFisUsZAQNKuEdFhiXei+5lcZ0QOxu5TJiKS26bDf2Fu3CkIAQwM8sayTpegTJilv5hV1USbiLCyKlk5Y7+/q7WbhoiI9AkhsDThLJb/+CcAYEy3ZlgwLAh2ihDgoSF6FVjh34MzIkT3YTJCRGSqMuXd1X7heCvuNLYe1d6intavNaY+2vrvkgcs8U5UKSYjRESmMFDePdeuMXLujIEkheGdYUF4tru/jAESWR4mI0RExiot716mqmr9kutY6RCD5PDl6MJEhMhkJtUZISKyWUaUd++S8j7LuxNVA5MRIiJjmFLenYhMwmSEiMgYLO9OVGuYjBARGYPl3YlqDZMRIiIjrL3kjauiITQVlomUtMXMWN6dyGRMRoiIKqHWCMz/+hTeiT+L+cWRkCRAoGyzGZZ3J3oQTEaIiCpwt1iNlzafwPqDfwEAggdEAiM2QlL56A9U+QIjNrK8O1E1sc4IERFQrqpqjkcoJm06gRNpN6G0U+DDZzpiWOcmAFoCgY+zvDtRDWIyQkRkoKpqidQIjQvHQuXUA6sjQ9G9RaO/x7O8O1GNYjJCRLatgqqqHppsrFLGIH1Ae/jen4gQUY3jmhEisl1VVFUFJPgens+qqkS1jMkIEdkuVlUlMgtMRojIdrGqKpFZYDJCRDYrz97ItSCsqkpUq5iMEJFN+jOzAMO+VrOqKpEZYDJCRDbnwLksPBF7EBdyCvGR4yRIkgSwqiqRbJiMEJFN2fJLGsatP4r8uyUI8W+A6VNegzRiI8CqqkSyYZ0RIrJOZSqqqv3CEb37LP574AIAYFhnX7z/VEc4OdhpE47AwayqSiQTJiNEZH0MVFTNtfPApTvPAgjDK/3aYMqjre7dnrmHVVWJZMNkhIisSwUVVeuXZGGlQwyOd1uGrv0GyxMbERnENSNEZD2qqKgqSRK6nvmAFVWJzAyTESKyHqyoSmSRmIwQkfVgRVUii8RkhIisRo7UwLiBrKhKZFaYjBCRVTiRdgODdpVoK6pWOIoVVYnMEZMRIrJ4OxIvYdTHR5BRUIL/urwACayoSmRJuLWXiCxDmSJm8O+BIo2EBd+cwqdH0gAAEe29MH3kAEjn25erMwKVrzYRYUVVIrPDZISIzJ+BImZqVx8sVUzAp5kPQZKAaY+2wb/7toJCIbGiKpGFYTJCROatgiJmUkE6Zoh3keH0KoaOisIjgZ7657GiKpHF4JoRIjJflRUxAwAJ+NB1Kx5p06iuIyOiGsRkhIjMVxVFzBQA7AuusogZkYVjMkJE5otFzIhsApMRIjJfxhYnYxEzIovGZISIzFKxWoP3TzfUFjErv2TkHhYxI7IGTEaIyOxk5N7F6DVHsHLfX5hfHAlJAgSLmBFZLW7tJSL5GChk9vOfOXhlezJybhXBzdEew56OgmQXwiJmRFaMyQgRycNAIbN8pSe23hqNHHUY2vuoEDumC5p7uABgETMiayYJISq8G2su8vLy4O7ujtzcXKhUKrnDIaIHVUEhs9K1IVubv4unnn0RTg5MNogsmbHf31wzQkR1q7JCZhIgSRLG3IiFE/MQIpvBZISI6lYVhcwkCCDvCguZEdkQJiNEVLdYyIyIymAyQkR16kSO0riBLGRGZDOYjBBRnSgsUWP+16fw9HeStpBZhSNZyIzI1jAZIaKao1EDF/YDJ3dq/9SoAQB/ZhZg+EeHsP7gX9BAgf0tX4MECWAhMyIC64wQUU0xUDdEqHxxsNUMPH/MF3eK1WjoosR/numIvoGDgRQ/FjIjIgCsM0JENaGCuiECgBDAi8XTUNBiIJaO6AxPldPfAwxUYOWMCJH1MPb7mzMjRPRgKqkbIt07+h+3rXAZPwcK+zL/yVHYAQG96yJKIjJjXDNCRA+mirohCglwK7wGxaXDdRgUEVkSJiNE9GBYN4SIHhCTESJ6IBoXT+MGsm4IEVWAyQgRVVtG7l2M/9FeWzekwqXwrBtCRJVjMkJElaugdsjXv17FgJh92PfnDURrxkOSJAjWDSGiauBuGiKqmIHaIRo3X2xQRWHB+VYAgI5N3TF1xKuQsoJZN4SIqqVaMyOxsbEICAiAk5MTQkJCsH///grHfvHFF+jfvz8aN24MlUqF8PBwfP/999UOmIjqSGntkLI7ZfKvYvzluRhodxRT+rbC5y/2QCtPV23CMe13YNw3wFNrtX9OO8lEhIiqZHIysn37dkybNg2zZ89GUlISevfujYEDByItLc3g+H379qF///6Ij4/H8ePH8cgjj2DIkCFISkp64OCJqJZUUjtEAQASsKz+dkzv1woOdvf9Z6S0bkiHp7V/8tYMERnB5Aqs3bp1Q5cuXbBy5UrdsXbt2mH48OGIjo426jUeeughjBw5EnPnzjVqPCuwEtWxC/uBTx6vety4b1i0jIgqZOz3t0kzI0VFRTh+/DgiIiL0jkdERODQoUNGvYZGo0F+fj4aNmxY4ZjCwkLk5eXpPYioDrF2CBHVIZOSkaysLKjVanh56dcL8PLyQkZGhlGvsXjxYty6dQsjRoyocEx0dDTc3d11Dz8/P1PCJKIHlHzT0biBrB1CRDWgWgtYJUl/+54QotwxQ7Zu3Yq3334b27dvh6dnxYWSZs2ahdzcXN3j0qVL1QmTiEyUd7cYb+z8DU9+C23tkApHsnYIEdUck7b2enh4wM7OrtwsSGZmZrnZkrK2b9+OiRMnYseOHejXr1+lYx0dHeHoaOS/zIjINBV0yt1zKgNzvzqFjLy7kCQFDrScgWdS37x30v1Ly1g7hIhqlknJiFKpREhICBISEvDEE0/ojickJGDYsGEVnrd161ZMmDABW7duxeDBg6sfLRE9GAN1Q9SuPljr9gLeu9AGANC8kTM+eLoTwgIGAylNWTuEiGqdyUXPpk+fjrFjxyI0NBTh4eFYvXo10tLSEBUVBUB7i+XKlSvYuHEjAG0iEhkZiWXLlqF79+66WZV69erB3d29Bj8KEVWqtG5Ime26UkE6JuW/jSS7VxDQexSmPNoaTg73ZjzaDwUCBxucSSEiqikmJyMjR45EdnY2FixYgPT0dAQFBSE+Ph7+/v4AgPT0dL2aIx9//DFKSkrw0ksv4aWXXtIdHzduHDZs2PDgn4CIqlZF3RCNBCyvvx0OEXPKJxqltUOIiGqJyXVG5MA6I0QPiHVDiEgGtVJnhIgsFOuGEJEZYzJCZOVu3i7CmuRbxg1m3RAikgG79hJZAwPbdTVQ4PMTlxH93RncvNUQgx0bwkfKgeGKQJJ2lwzrhhCRDJiMEFk6A9t1i118EOMwER9ltAcAtPFSoaDzQkg/ly4iZ90QIjIfTEaILFkF23XtCtLxKhbiknI6gvo9i+d6Bmi763q5sW4IEZkd7qYhslQaNRATpJ9Y3EcAULv6wn767/ozHhVUYCUiqmnGfn9zZoTIUl08VGEiAmhvvtgXXNWOu3+7LuuGEJGZ4W4aIgt1O/uKcQO5XZeIzBxnRojMUSW3UtQaga1H07D3+3T815jX4nZdIjJzTEaIzI2B3THaRabv44hTT7wddwpnMvKhQCtcr9cIHiIHkoEy79yuS0SWgskIkTmpYHeMyEsHPhuL9UXTcEYTBpWTPab3b4OG7ksh7RwH7QoRbtclIsvEZITIXFTSzE6CgEYA8xw2wbPzE3gloj0auigBBACKjdyuS0QWjckIkbmoYneMQgJ8kY13OucDLsq/n2g/FAgczO26RGSxmIwQmYsHaWbH7bpEZMG4tZfITPx5x8W4gdwdQ0RWhjMjRHWhkq26l3Ju48Pv/8A3v5bggGNDeCMHCoPd7Lg7hoisE5MRotpWwVbd/EfexbIrgdh4+CKK1BpIkgLfN30F46/MvTeIu2OIyDYwGSGqTRVu1b0Kl13P4VLxNBRpwtCzVSPMGtgOQU0GAynNuTuGiGwKG+UR1ZYqGtlpBJBt54FTzxxAn0BvSJKkfy53xxCRhWOjPCK5GbFVt7EmCw87/QlIPmWe5O4YIrId3E1DVEvUeenGDWQjOyKycZwZIaquCm6llKg1+Cr5KvYnXEOMMa/DrbpEZOOYjBBVh4EdMsLNF4fazMCbZwJwMfs2FGiOmU6N4AU2siMiqgxv0xCZqnSHTJn1ICL/KsITX0Hgjb1o6KLEjMfaw/3Jxfc25ZYtHMKtukREpTgzQmSKSprZKQBoJGCx21ZI096ESz1HAC0Beztu1SUiqgSTESJTVLVDBoBr4TUg4+jfu2HYyI6IqFJMRohKVVHbI+dWEY4cTsYgY16r7A4ZbtUlIqoQkxEioMKS7XjsfVzx7Y81+1Kx/dgldFLfxSClEa/HHTJEREZjMkJUYcn2dOCzsXi3+BXEq7sCAG75dMWdu95wunONO2SIiGoIkxGybZUsSJUgoBHAW/YbkevfH1GPtEGvVh6QTn94L3mRwGZ2REQPjlt7ybYZUbLdV8rG5v4a9G7dWNs/pv1QYMRGQFWmhLvKV3ucO2SIiEzCmRGyblUsSs29fgnuxrxO2QWp3CFDRFRjmIyQ9apkUeqp+n2w7sBfuPbbVXxqzG+BoQWp3CFDRFQjmIyQdapiUeryomn4XhMGBdoiS+mBRppsLkglIpIJ14yQ9aliUaoQwDyHTRja0QufT+4Fj6eXsmQ7EZGMmIyQZdGogQv7gZM7tX9q1OXHGLkodXn4HQQ3a8AFqUREMuNtGrIclawBKU0Yrt68g9+OJOMxY17v/kWpXJBKRCQbJiNkGSpYA4K8dIjPInGi2zIsT2+Hfeeuo5t0F49Vp0oqF6QSEcmCt2nI/FWyBgQQEBDwOTIf+89egxAAmoXjtpMXRLk1IKUkQNWEi1KJiMwEZ0bI/BnRKddXysZ7XfLQve9wNPdwAVL+wyqpREQWgjMjJL8qFqUW5aYb9TKj2jlqExGAi1KJiCwIZ0ZIXhUsSlUPWIQjjj2xK+kKsn6/jPUV3XG5X9k1IFyUSkRkEZiMkHwqLEx2FYodkdioK0zWGtecGsET2RWsAqmkMBkXpRIRmT0mI1TzqugHoxuz+w0IA8tMJQAaAbyt3ASPjk9gWHAzNL69FNKOcfdGcA0IEZE1YTJCNcuIWiAajcC5o9+jbd7VCve7KCTAB9l4NzgfCGgIYBggbazgtRdxDQgRkQVjMkI1p4paIH/0+Qjb8jtj9+8ZCCs4iOXG1AJhYTIiIqvHZISMU9WtlyprgQCqvXOwsXAZNFAg37GRce/LwmRERFaPyQhVzYhbL8bWAnmtbTbadBuIXi37Ax+tAfLSYTiBYbdcIiJbwTojVLnSWy9lE428dOCzSNz97Uv8eOYadv6caNTLTQ51Rb/2XnByVGqTGQDslktEZNuYjNgqY7rfVnHrRQOBnM9fxaQNR7HzbIlx73v/bRcWJiMiIvA2jW0y5rYLYPStl8GqC1AF9sedc/+F051rkEy57cJFqURENo/JiK2pZMcLPouEGPEJ/mzUF0cu5KAk+QieM+Illz/uA6ljZyDlw+r1g+GiVCIim8ZkxFqYUGissh0v1z57BQPuane8dFcAzxmx/VZy89b+j9LbLqwFQkREJmAyYg2MvO0iLh6EVMltFwmAN7LR0+EPqJv1QvfmQ1CY9F8ob5tw64W3XYiIyERMRsyZMbMdVRQaO9VrBX62C8fJy7lo/NcPeMeIt133VDM4dO6u/aFJNW698LYLERGZgMlIXTImuShlzGxHJf1dAAEhgIb752FxYeltF1fAiNsuDu737W7hrRciIqplTEYelLEJhrE7WErHGuxmq11k+nuvFTii7Al16j5EVdHfxRfZmNrqOhxb90Fwk67QfLUOinwTC43x1gsREdUiJiNl1fTsRem4Snaw6NXU0Kih+e4NSAa72QpoBNBo/zxEFy7D44pzRs10TO2mAjq01P4w8H3ueCEiIrNSraJnsbGxCAgIgJOTE0JCQrB///5Kx//8888ICQmBk5MTWrRogVWrVlUr2FqXEgfEBAGfPA58PlH7Z0yQ9rihsZVUJtWdY8QOlrxdr+HlzccwZMUBTFiwDIr8KmY7pGxMaXkdvbsEGfe5WGiMiIjMmMkzI9u3b8e0adMQGxuLnj174uOPP8bAgQORkpKCZs2alRt/4cIFDBo0CM8//zw+/fRTHDx4EJMnT0bjxo3x1FNP1ciHqBEmzl5UnmBIuPP1DGzPbo966b9gVKU7WARURdeQdWovTmraY6gi26jZjmndVcBDTwBpC0zv78LbLkREZEYkIYShb7EKdevWDV26dMHKlSt1x9q1a4fhw4cjOjq63Pg33ngDcXFxOH36tO5YVFQUfv31Vxw+fNio98zLy4O7uztyc3OhUqlMCbdSubeLkXe3GIVFxfDf1A32t9INzkgISChQemJZh8+RV6iBz41EvHJlepWvP6roLXjiJpYr/6/KsT8+9B5K2j+FwLu/otnXI6oOftw32tsmuiRKG+nf7n0SznYQEZFMjP3+NmlmpKioCMePH8fMmTP1jkdERODQoUMGzzl8+DAiIiL0jg0YMABr165FcXExHBwcyp1TWFiIwsJCvQ9TG9788iS+PZmO7ooUbFOmVzhOgoBb0TX8fng3jmjaY6gi1ajZi4hmAFzbAn9WPbZvaEcgwBvQNAZ+9jV+toO7XYiIyMKZlIxkZWVBrVbDy8tL77iXlxcyMjIMnpORkWFwfElJCbKysuDj41PunOjoaMyfP9+U0KrFycEOTg4KNLfPN/y9X8Y/2ynRu2lbtLx1GzCiSe2EAd21SUNMtPHJhcJOuwDWlEWmvO1CREQWrFoLWCVJ/2aGEKLcsarGGzpeatasWcjNzdU9Ll26VJ0wq7R4RCeceWcgFkX2N2r8sF5d8NIjrfDYoCe1CUSFy0wlQNXk74Tgsff/Pl52HGA4uTB1kWnpbpcOT2v/ZCJCREQWwqSZEQ8PD9jZ2ZWbBcnMzCw3+1HK29vb4Hh7e3s0atTI4DmOjo5wdHQ0JbQH499D+0VfW7MX1bmVwtkOIiKyESYlI0qlEiEhIUhISMATTzyhO56QkIBhw4YZPCc8PBxff/213rE9e/YgNDTU4HoRWVT31ogpCUZ1kgvW9iAiIhtg8m6a7du3Y+zYsVi1ahXCw8OxevVqrFmzBqdOnYK/vz9mzZqFK1euYOPGjQC0W3uDgoLwwgsv4Pnnn8fhw4cRFRWFrVu3Gr21t7Z205RjsIhZk8oXgppSJI2IiMiG1MpuGgAYOXIksrOzsWDBAqSnpyMoKAjx8fHw9/cHAKSnpyMtLU03PiAgAPHx8XjllVfw0UcfwdfXF8uXLzevGiOlOHtBRERU50yeGZFDnc2MEBERUY0x9vu7WrtpiIiIiGoKkxEiIiKSFZMRIiIikhWTESIiIpIVkxEiIiKSFZMRIiIikhWTESIiIpIVkxEiIiKSFZMRIiIikpXJ5eDlUFokNi8vT+ZIiIiIyFil39tVFXu3iGQkPz8fAODn5ydzJERERGSq/Px8uLu7V/i8RfSm0Wg0uHr1Ktzc3CBJUrVeIy8vD35+frh06RL729QBXu+6x2tet3i96x6ved2qiesthEB+fj58fX2hUFS8MsQiZkYUCgWaNm1aI6+lUqn4l7gO8XrXPV7zusXrXfd4zevWg17vymZESnEBKxEREcmKyQgRERHJymaSEUdHR8ybNw+Ojo5yh2ITeL3rHq953eL1rnu85nWrLq+3RSxgJSIiIutlMzMjREREZJ6YjBAREZGsmIwQERGRrJiMEBERkaysJhmJjY1FQEAAnJycEBISgv3791c6/ueff0ZISAicnJzQokULrFq1qo4itR6mXPMvvvgC/fv3R+PGjaFSqRAeHo7vv/++DqO1fKb+HS918OBB2Nvbo3PnzrUboBUy9ZoXFhZi9uzZ8Pf3h6OjI1q2bIl169bVUbSWz9TrvXnzZnTq1AnOzs7w8fHBc889h+zs7DqK1vLt27cPQ4YMga+vLyRJwq5du6o8p9a+O4UV2LZtm3BwcBBr1qwRKSkpYurUqcLFxUVcvHjR4PjU1FTh7Owspk6dKlJSUsSaNWuEg4OD2LlzZx1HbrlMveZTp04V77//vjh69Kg4e/asmDVrlnBwcBAnTpyo48gtk6nXu9TNmzdFixYtREREhOjUqVPdBGslqnPNhw4dKrp16yYSEhLEhQsXxC+//CIOHjxYh1FbLlOv9/79+4VCoRDLli0TqampYv/+/eKhhx4Sw4cPr+PILVd8fLyYPXu2+PzzzwUA8eWXX1Y6vja/O60iGQkLCxNRUVF6xwIDA8XMmTMNjn/99ddFYGCg3rEXXnhBdO/evdZitDamXnND2rdvL+bPn1/ToVml6l7vkSNHirfeekvMmzePyYiJTL3m3333nXB3dxfZ2dl1EZ7VMfV6f/jhh6JFixZ6x5YvXy6aNm1aazFaM2OSkdr87rT42zRFRUU4fvw4IiIi9I5HRETg0KFDBs85fPhwufEDBgxAYmIiiouLay1Wa1Gda16WRqNBfn4+GjZsWBshWpXqXu/169fj/PnzmDdvXm2HaHWqc83j4uIQGhqKDz74AE2aNEGbNm3w2muv4c6dO3URskWrzvXu0aMHLl++jPj4eAghcO3aNezcuRODBw+ui5BtUm1+d1pEo7zKZGVlQa1Ww8vLS++4l5cXMjIyDJ6TkZFhcHxJSQmysrLg4+NTa/Fag+pc87IWL16MW7duYcSIEbURolWpzvU+d+4cZs6cif3798Pe3uJ/zetcda55amoqDhw4ACcnJ3z55ZfIysrC5MmTkZOTw3UjVajO9e7Rowc2b96MkSNH4u7duygpKcHQoUOxYsWKugjZJtXmd6fFz4yUkiRJ72chRLljVY03dJwqZuo1L7V161a8/fbb2L59Ozw9PWsrPKtj7PVWq9UYPXo05s+fjzZt2tRVeFbJlL/jGo0GkiRh8+bNCAsLw6BBg7BkyRJs2LCBsyNGMuV6p6SkYMqUKZg7dy6OHz+O3bt348KFC4iKiqqLUG1WbX13Wvw/mTw8PGBnZ1cue87MzCyXwZXy9vY2ON7e3h6NGjWqtVitRXWueant27dj4sSJ2LFjB/r161ebYVoNU693fn4+EhMTkZSUhJdffhmA9otSCAF7e3vs2bMHffv2rZPYLVV1/o77+PigSZMmeu3S27VrByEELl++jNatW9dqzJasOtc7OjoaPXv2xIwZMwAAHTt2hIuLC3r37o2FCxdyhrsW1OZ3p8XPjCiVSoSEhCAhIUHveEJCAnr06GHwnPDw8HLj9+zZg9DQUDg4ONRarNaiOtcc0M6IjB8/Hlu2bOF9XROYer1VKhVOnjyJ5ORk3SMqKgpt27ZFcnIyunXrVlehW6zq/B3v2bMnrl69ioKCAt2xs2fPQqFQoGnTprUar6WrzvW+ffs2FAr9rzA7OzsAf/9rnWpWrX53PvASWDNQuiVs7dq1IiUlRUybNk24uLiIv/76SwghxMyZM8XYsWN140u3J73yyisiJSVFrF27llt7TWTqNd+yZYuwt7cXH330kUhPT9c9bt68KddHsCimXu+yuJvGdKZe8/z8fNG0aVPx9NNPi1OnTomff/5ZtG7dWkyaNEmuj2BRTL3e69evF/b29iI2NlacP39eHDhwQISGhoqwsDC5PoLFyc/PF0lJSSIpKUkAEEuWLBFJSUm67dR1+d1pFcmIEEJ89NFHwt/fXyiVStGlSxfx888/654bN26c6NOnj974vXv3iuDgYKFUKkXz5s3FypUr6zhiy2fKNe/Tp48AUO4xbty4ug/cQpn6d/x+TEaqx9Rrfvr0adGvXz9Rr1490bRpUzF9+nRx+/btOo7acpl6vZcvXy7at28v6tWrJ3x8fMSYMWPE5cuX6zhqy/XTTz9V+t/luvzulITgfBYRERHJx+LXjBAREZFlYzJCREREsmIyQkRERLJiMkJERESyYjJCREREsmIyQkRERLJiMkJERESyYjJCREREsmIyQkRERLJiMkJERESyYjJCREREsmIyQkR17vr16/D29sZ7772nO/bLL79AqVRiz549MkZGRHJgozwikkV8fDyGDx+OQ4cOITAwEMHBwRg8eDBiYmLkDo2I6hiTESKSzUsvvYT//e9/6Nq1K3799VccO3YMTk5OcodFRHWMyQgRyebOnTsICgrCpUuXkJiYiI4dO8odEhHJgGtGiEg2qampuHr1KjQaDS5evCh3OEQkE86MEJEsioqKEBYWhs6dOyMwMBBLlizByZMn4eXlJXdoRFTHmIwQkSxmzJiBnTt34tdff4WrqyseeeQRuLm54ZtvvpE7NCKqY7xNQ0R1bu/evYiJicGmTZugUqmgUCiwadMmHDhwACtXrpQ7PCKqY5wZISIiIllxZoSIiIhkxWSEiIiIZMVkhIiIiGTFZISIiIhkxWSEiIiIZMVkhIiIiGTFZISIiIhkxWSEiIiIZMVkhIiIiGTFZISIiIhkxWSEiIiIZPX/TiJq15Qhb4EAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_edge = macro_mesh.edges[1:-1]  # note that grad_u_disc is evaluated on the node edges\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x_fine, x_fine**2, x_edge, grad_u_disc.evaluate(y=y), \"o\")\n",
    "ax.set_xlabel(\"x\")\n",
    "legend = ax.legend([\"x^2\", \"grad(u).evaluate(y=x**3/3)\"], loc=\"best\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similary, we can create, discretise and evaluate the gradient of `v`, which is a variable in the negative particles. Note that the syntax for doing this is identical: we do not need to explicitly specify that we want the gradient in `r`, since this is inferred from the `domain` of `v`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['negative particle']"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.domain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "grad(v) tree is:\n",
      "\n",
      "@\n",
      "├── Sparse Matrix (9, 10)\n",
      "└── y[40:50]\n",
      "\n",
      " gradient matrix is:\n",
      "\n",
      "1/dr *\n",
      "[[-1.  1.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0. -1.  1.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0. -1.  1.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0. -1.  1.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0. -1.  1.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0. -1.  1.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0. -1.  1.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0. -1.  1.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0. -1.  1.]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grad_v = pybamm.grad(v)\n",
    "grad_v_disc = disc.process_symbol(grad_v)\n",
    "print(\"grad(v) tree is:\\n\")\n",
    "grad_v_disc.render()\n",
    "\n",
    "micro_mesh = mesh[\"negative particle\"]\n",
    "print(\"\\n gradient matrix is:\\n\")\n",
    "print(\n",
    "    f\"1/dr *\\n{micro_mesh.d_nodes[:, np.newaxis] * grad_v_disc.children[0].entries.toarray()}\"\n",
    ")\n",
    "\n",
    "r_edge = micro_mesh.edges[1:-1]  # note that grad_u_disc is evaluated on the node edges\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(r_fine, -np.sin(r_fine), r_edge, grad_v_disc.evaluate(y=y), \"o\")\n",
    "ax.set_xlabel(\"x\")\n",
    "legend = ax.legend([\"-sin(r)\", \"grad(v).evaluate(y=cos(r))\"], loc=\"best\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Boundary conditions"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the discretisation is provided with boundary conditions, appropriate ghost nodes are concatenated onto the variable, and a larger gradient matrix is used. The ghost nodes are chosen based on the value of the first/last node in the variable and the boundary condition.\n",
    "For a Dirichlet boundary condition $u=a$ on the left-hand boundary, we set the value of the left ghost node to be equal to\n",
    "$$2*a-u[0],$$\n",
    "where $u[0]$ is the value of $u$ in the left-most cell in the domain. Similarly, for a Dirichlet condition $u=b$ on the right-hand boundary, we set the right ghost node to be\n",
    "$$2*b-u[-1].$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The gradient object is:\n",
      "+\n",
      "├── Column vector of length 41\n",
      "└── @\n",
      "    ├── Sparse Matrix (41, 40)\n",
      "    └── y[0:40]\n",
      "The value of u on the left-hand boundary is [1.]\n",
      "The value of u on the right-hand boundary is [1.67902865]\n"
     ]
    }
   ],
   "source": [
    "disc.bcs = {\n",
    "    u: {\n",
    "        \"left\": (pybamm.Scalar(1), \"Dirichlet\"),\n",
    "        \"right\": (pybamm.Scalar(2), \"Dirichlet\"),\n",
    "    }\n",
    "}\n",
    "grad_u_disc = disc.process_symbol(grad_u)\n",
    "print(\"The gradient object is:\")\n",
    "(grad_u_disc.render())\n",
    "u_eval = grad_u_disc.evaluate(y=y)\n",
    "dx = np.diff(macro_mesh.nodes)[-1]\n",
    "print(f\"The value of u on the left-hand boundary is {y[0] - dx * u_eval[0] / 2}\")\n",
    "print(f\"The value of u on the right-hand boundary is {y[1] + dx * u_eval[-1] / 2}\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a Neumann boundary condition $\\partial u/\\partial x=c$ on the left-hand boundary, we set the value of the left ghost node to be\n",
    "$$u[0] - c * dx,$$\n",
    "where $dx$ is the step size at the left-hand boundary. For a Neumann boundary condition $\\partial u/\\partial x=d$ on the right-hand boundary, we set the value of the right ghost node to be\n",
    "$$u[-1] + d * dx.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The gradient object is:\n",
      "+\n",
      "├── Column vector of length 41\n",
      "└── @\n",
      "    ├── Sparse Matrix (41, 40)\n",
      "    └── y[0:40]\n",
      "The gradient on the left-hand boundary is [3.]\n",
      "The gradient of u on the right-hand boundary is [4.]\n"
     ]
    }
   ],
   "source": [
    "disc.bcs = {\n",
    "    u: {\"left\": (pybamm.Scalar(3), \"Neumann\"), \"right\": (pybamm.Scalar(4), \"Neumann\")}\n",
    "}\n",
    "grad_u_disc = disc.process_symbol(grad_u)\n",
    "print(\"The gradient object is:\")\n",
    "(grad_u_disc.render())\n",
    "grad_u_eval = grad_u_disc.evaluate(y=y)\n",
    "print(f\"The gradient on the left-hand boundary is {grad_u_eval[0]}\")\n",
    "print(f\"The gradient of u on the right-hand boundary is {grad_u_eval[-1]}\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can mix the types of the boundary conditions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The gradient object is:\n",
      "+\n",
      "├── Column vector of length 41\n",
      "└── @\n",
      "    ├── Sparse Matrix (41, 40)\n",
      "    └── y[0:40]\n",
      "The value of u on the left-hand boundary is [0.00036458]\n",
      "The gradient on the right-hand boundary is [6.]\n"
     ]
    }
   ],
   "source": [
    "disc.bcs = {\n",
    "    u: {\"left\": (pybamm.Scalar(5), \"Dirichlet\"), \"right\": (pybamm.Scalar(6), \"Neumann\")}\n",
    "}\n",
    "grad_u_disc = disc.process_symbol(grad_u)\n",
    "print(\"The gradient object is:\")\n",
    "(grad_u_disc.render())\n",
    "grad_u_eval = grad_u_disc.evaluate(y=y)\n",
    "u_eval = grad_u_disc.children[1].evaluate(y=y)\n",
    "print(f\"The value of u on the left-hand boundary is {(u_eval[0] + u_eval[1]) / 2}\")\n",
    "print(f\"The gradient on the right-hand boundary is {grad_u_eval[-1]}\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Robin boundary conditions can be implemented by specifying a Neumann condition where the flux depends on the variable."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Divergence operator"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before computing the Divergence operator, we set up Neumann boundary conditions. The behaviour with Dirichlet boundary conditions is very similar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "disc.bcs = {\n",
    "    u: {\"left\": (pybamm.Scalar(-1), \"Neumann\"), \"right\": (pybamm.Scalar(1), \"Neumann\")}\n",
    "}"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can process `div(grad(u))`, converting it to a Matrix-Vector multiplication, plus a vector for the boundary conditions. Since we have Neumann boundary conditions, the divergence of an object of size (n+1,) has size (n,), and so div(grad) of an object of size (n,) has size (n,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+\n",
      "├── Column vector of length 40\n",
      "└── @\n",
      "    ├── Sparse Matrix (40, 40)\n",
      "    └── y[0:40]\n"
     ]
    }
   ],
   "source": [
    "div_grad_u = pybamm.div(grad_u)\n",
    "div_grad_u_disc = disc.process_symbol(div_grad_u)\n",
    "div_grad_u_disc.render()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The div(grad) matrix is automatically simplified to the well-known `[1,-2,1]` matrix (divided by the square of the distance between the edges), except in the first and last rows for boundary conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "div(grad) matrix is:\n",
      "\n",
      "1/dx^2 * \n",
      "[[-1.  1.  0. ...  0.  0.  0.]\n",
      " [ 1. -2.  1. ...  0.  0.  0.]\n",
      " [ 0.  1. -2. ...  0.  0.  0.]\n",
      " ...\n",
      " [ 0.  0.  0. ... -2.  1.  0.]\n",
      " [ 0.  0.  0. ...  1. -2.  1.]\n",
      " [ 0.  0.  0. ...  0.  1. -1.]]\n"
     ]
    }
   ],
   "source": [
    "print(\"div(grad) matrix is:\\n\")\n",
    "print(\n",
    "    \"1/dx^2 * \\n{}\".format(\n",
    "        macro_mesh.d_edges[:, np.newaxis] ** 2\n",
    "        * div_grad_u_disc.right.left.entries.toarray()\n",
    "    )\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integral operator"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can define an integral operator, which integrates the variable across the domain specified by the integration variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "int(u) = [[0.08330729]] is approximately equal to 1/12, 0.08333333333333333\n",
      "int(v/r^2) = [[11.07985772]] is approximately equal to 4 * pi * sin(1), 10.574236256325824\n"
     ]
    }
   ],
   "source": [
    "int_u = pybamm.Integral(u, x_var)\n",
    "int_u_disc = disc.process_symbol(int_u)\n",
    "print(f\"int(u) = {int_u_disc.evaluate(y=y)} is approximately equal to 1/12, {1 / 12}\")\n",
    "\n",
    "# We divide v by r to evaluate the integral more easily\n",
    "int_v_over_r2 = pybamm.Integral(v / r_var**2, r_var)\n",
    "int_v_over_r2_disc = disc.process_symbol(int_v_over_r2)\n",
    "print(\n",
    "    f\"int(v/r^2) = {int_v_over_r2_disc.evaluate(y=y)} is approximately equal to 4 * pi * sin(1), {4 * np.pi * np.sin(1)}\"\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The integral operators are also Matrix-Vector multiplications"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "int(u):\n",
      "\n",
      "@\n",
      "├── Sparse Matrix (1, 40)\n",
      "└── y[0:40]\n",
      "\n",
      "int(v):\n",
      "\n",
      "@\n",
      "├── Sparse Matrix (1, 10)\n",
      "└── *\n",
      "    ├── Column vector of length 10\n",
      "    └── y[40:50]\n"
     ]
    }
   ],
   "source": [
    "print(\"int(u):\\n\")\n",
    "int_u_disc.render()\n",
    "print(\"\\nint(v):\\n\")\n",
    "int_v_over_r2_disc.render()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "         1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "         1., 1., 1., 1., 1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_u_disc.children[0].evaluate() / macro_mesh.d_edges"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discretising a model"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now discretise a whole model. We create, and discretise, a simple model for the concentration in the electrolyte and the concentration in the particles, and discretise it with a single command:\n",
    "```\n",
    "disc.process_model(model)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = pybamm.BaseModel()\n",
    "\n",
    "c_e = pybamm.Variable(\"electrolyte concentration\", domain=macroscale)\n",
    "N_e = pybamm.grad(c_e)\n",
    "c_s = pybamm.Variable(\"particle concentration\", domain=[\"negative particle\"])\n",
    "N_s = pybamm.grad(c_s)\n",
    "model.rhs = {c_e: pybamm.div(N_e) - 5, c_s: pybamm.div(N_s)}\n",
    "model.boundary_conditions = {\n",
    "    c_e: {\"left\": (np.cos(0), \"Neumann\"), \"right\": (np.cos(10), \"Neumann\")},\n",
    "    c_s: {\"left\": (0, \"Neumann\"), \"right\": (-1, \"Neumann\")},\n",
    "}\n",
    "model.initial_conditions = {c_e: 1 + 0.1 * pybamm.sin(10 * x_var), c_s: 1}\n",
    "\n",
    "# Create a new discretisation and process model\n",
    "disc2 = pybamm.Discretisation(mesh, spatial_methods)\n",
    "disc2.process_model(model);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The initial conditions are discretised to vectors, and an array of concatenated initial conditions is created."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1300x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c_e_0 = model.initial_conditions[c_e].evaluate()\n",
    "c_s_0 = model.initial_conditions[c_s].evaluate()\n",
    "y0 = model.concatenated_initial_conditions.evaluate()\n",
    "\n",
    "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(13, 4))\n",
    "ax1.plot(x_fine, 1 + 0.1 * np.sin(10 * x_fine), x, c_e_0, \"o\")\n",
    "ax1.set_xlabel(\"x\")\n",
    "ax1.legend([\"1+0.1*sin(10*x)\", \"c_e_0\"], loc=\"best\")\n",
    "\n",
    "ax2.plot(x_fine, np.ones_like(r_fine), r, c_s_0, \"o\")\n",
    "ax2.set_xlabel(\"r\")\n",
    "ax2.legend([\"1\", \"c_s_0\"], loc=\"best\")\n",
    "\n",
    "ax3.plot(y0, \"*\")\n",
    "ax3.set_xlabel(\"index\")\n",
    "ax3.set_ylabel(\"y0\")\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The discretised rhs can be evaluated, for example at `0,y0`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1300x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rhs_c_e = model.rhs[c_e].evaluate(0, y0)\n",
    "rhs_c_s = model.rhs[c_s].evaluate(0, y0)\n",
    "rhs = model.concatenated_rhs.evaluate(0, y0)\n",
    "\n",
    "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(13, 4))\n",
    "ax1.plot(x_fine, -10 * np.sin(10 * x_fine) - 5, x, rhs_c_e, \"o\")\n",
    "ax1.set_xlabel(\"x\")\n",
    "ax1.set_ylabel(\"rhs_c_e\")\n",
    "ax1.legend([\"1+0.1*sin(10*x)\", \"c_e_0\"], loc=\"best\")\n",
    "\n",
    "ax2.plot(r, rhs_c_s, \"o\")\n",
    "ax2.set_xlabel(\"r\")\n",
    "ax2.set_ylabel(\"rhs_c_s\")\n",
    "\n",
    "ax3.plot(rhs, \"*\")\n",
    "ax3.set_xlabel(\"index\")\n",
    "ax3.set_ylabel(\"rhs\")\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `model.concatenated_rhs` is then passed to the solver to solve the model, with initial conditions `model.concatenated_initial_conditions`."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Upwinding and downwinding"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If a system is advection-dominated (Peclet number greater than around 40), then it is important to use upwinding (if velocity is positive) or downwinding (if velocity is negative) to obtain accurate results. To see this, consider the following model (without upwinding)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a8807565aaf548f48ddf00a2e1d3f865",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='t', step=1.0), Output()), _dom_classes=('widget-inte…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = pybamm.BaseModel()\n",
    "\n",
    "# Define concentration and velocity\n",
    "c = pybamm.Variable(\n",
    "    \"c\", domain=[\"negative electrode\", \"separator\", \"positive electrode\"]\n",
    ")\n",
    "v = pybamm.PrimaryBroadcastToEdges(\n",
    "    1, [\"negative electrode\", \"separator\", \"positive electrode\"]\n",
    ")\n",
    "model.rhs = {c: -pybamm.div(c * v) + 1}\n",
    "model.initial_conditions = {c: 0}\n",
    "model.boundary_conditions = {c: {\"left\": (0, \"Dirichlet\")}}\n",
    "model.variables = {\"c\": c}\n",
    "\n",
    "\n",
    "def solve_and_plot(model):\n",
    "    model_disc = disc.process_model(model, inplace=False)\n",
    "\n",
    "    t_eval = [0, 100]\n",
    "    solution = pybamm.IDAKLUSolver().solve(model_disc, t_eval)\n",
    "\n",
    "    # plot\n",
    "    plot = pybamm.QuickPlot(solution, [\"c\"], spatial_unit=\"m\")\n",
    "    plot.dynamic_plot()\n",
    "\n",
    "\n",
    "solve_and_plot(model)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The concentration grows indefinitely, which is clearly an incorrect solution. Instead, we can use upwinding:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b50896a3c984451282cb4f0efb8389c9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='t', step=1.0), Output()), _dom_classes=('widget-inte…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.rhs = {c: -pybamm.div(pybamm.upwind(c) * v) + 1}\n",
    "solve_and_plot(model)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This gives the expected linear steady state from 0 to 1. Similarly, if the velocity is negative, downwinding gives accurate results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a40d1df3cf9745d78ca7b1450ce128b3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='t', step=1.0), Output()), _dom_classes=('widget-inte…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.rhs = {c: -pybamm.div(pybamm.downwind(c) * (-v)) + 1}\n",
    "model.boundary_conditions = {c: {\"right\": (0, \"Dirichlet\")}}\n",
    "solve_and_plot(model)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More advanced concepts"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since this notebook is only an introduction to the discretisation, we have not covered everything. More advanced concepts, such as the ones below, can be explored by looking into the [API docs](https://docs.pybamm.org/en/latest/source/api/solvers/index.html).\n",
    "\n",
    "- Gradient and divergence of microscale variables in the P2D model\n",
    "- Indefinite integral\n",
    "\n",
    "If you would like detailed examples of these operations, please [create an issue](https://docs.pybamm.org/en/latest/source/user_guide/contributing.html#a-before-you-begin) and we will be happy to help."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "The relevant papers for this notebook are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] Joel A. E. Andersson, Joris Gillis, Greg Horn, James B. Rawlings, and Moritz Diehl. CasADi – A software framework for nonlinear optimization and optimal control. Mathematical Programming Computation, 11(1):1–36, 2019. doi:10.1007/s12532-018-0139-4.\n",
      "[2] Charles R. Harris, K. Jarrod Millman, Stéfan J. van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J. Smith, and others. Array programming with NumPy. Nature, 585(7825):357–362, 2020. doi:10.1038/s41586-020-2649-2.\n",
      "[3] Valentin Sulzer, Scott G. Marquis, Robert Timms, Martin Robinson, and S. Jon Chapman. Python Battery Mathematical Modelling (PyBaMM). Journal of Open Research Software, 9(1):14, 2021. doi:10.5334/jors.309.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "pybamm.print_citations()"
   ]
  }
 ],
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